چکیده انگلیسی

This paper incorporates limited asset markets participation in dynamic general equilibrium and develops a simple analytical framework for monetary policy analysis. Aggregate dynamics and stability properties of an otherwise standard business cycle model depend nonlinearly on the degree of asset market participation. While ‘moderate’ participation rates strengthen the role of monetary policy, low enough participation causes an inversion of results dictated by conventional wisdom. The slope of the ‘IS’ curve changes sign, the ‘Taylor principle’ is inverted, optimal welfare-maximizing discretionary monetary policy requires a passive policy rule and the effects and propagation of shocks are changed. However, a targeting rule implementing optimal policy under commitment delivers equilibrium determinacy regardless of the degree of asset market participation. Our results may justify Fed's behavior during the ‘Great Inflation’ period.

مقدمه انگلیسی

At the heart of modern macroeconomic literature dealing with monetary policy issues lies
some form of ‘aggregate Euler equation’, or ‘IS’ curve: an inverse relationship between aggregate
consumption today and the expected real interest rate. This relationship is derived fromthe households’ individual Euler equations assuming that all households substitute consumption
intertemporally—for example using assets. Normative prescriptions are then derived by using
this equation as a building block, together with an inflation dynamics equation (‘Phillips curve’)
derived under the assumption of imperfect price adjustment. 1
This paper introduces limited asset markets participation (LAMP) into an otherwise standard
dynamic general equilibrium model and studies the implications of this for monetary policy. We
model LAMP in a way that has become standard in the macroeconomic literature reviewed below.
Namely, we assume that a fraction of agents have zero asset holdings, and hence do not smooth
consumption but merely consume their current disposable income, while the rest of the agents
hold all assets and smooth consumption. 2 This modelling choice is motivated both by direct
data on asset holdings and by an extensive empirical literature studying consumption behavior.
The latter seems to suggest that, regardless of whether aggregate time series or micro data are
used, consumption tracks current income for a large fraction of the US population. To give just
some prominent examples, Campbell and Mankiw [11] used aggregate time series data to find
that a fraction of 0.4 to 0.5 of the US population merely consumed their current income. More
recent studies using micro data also find that a significant fraction of the US population fails to
behave as prescribed by the permanent income hypothesis (e.g. [25,28]). 3 Finally, direct data on
asset holdings shows that a low fraction of US population holds assets in various forms. 4 Models
incorporating this insight have been recently used in the macroeconomic literature. First, some
version of this assumption—whereby a fraction of agents does not hold physical capital- has been
proposed by Mankiw [34] and extended by Gali et al. [20] for fiscal policy issues. 5 Second, it
is the norm in the monetary policy literature trying to capture the ‘liquidity effect’, where it is
assumed that asset markets are ‘segmented’ (e.g. Alvarez et al. [1]). This modelling choice has
only recently been incorporated into the sticky-price monetary policy research in a paper that we
review in detail below.
We show how the general equilibrium model with LAMP can be reduced to a familiar 2-
equations system, consisting of a Phillips- and an IS- curve, which nests the standard New Keynesian
model; since the resulting system is very simple, it might be of independent interest to
some researchers. Notably, we capture the influence of LAMP on aggregate dynamics through
an unique parameter, the elasticity of aggregate demand to real interest rates, which depends
non-linearly on the degree of asset market participation and is at the core of the intuition for all
our results. In a nutshell, we show that limited asset market participation has a non-linear effect
on most predictions of the standard full-participation model.Interest rate changes modify the intertemporal consumption and labor supply profile of asset
holders, agents who smooth consumption by trading in asset markets. This affects the real wage
and hence the demand of agents who have no asset holdings but merely consume their wage
income. Variations in the real wage (marginal cost) lead to variations in profits and hence in the
dividend income of asset holders. These variations can either reinforce (if participation is not ‘too’
limited) or overturn the initial impact of interest rates on aggregate demand. The latter case occurs
if the share of non-asset holders is high enough and/or and the elasticity of labor supply is low
enough, for the potential variations in profit income offset the interest rate effects on the demand
of asset holders. This is the main mechanism identified by this paper to change dramatically the
effects of monetary policy as compared to a standard full-participation case whereby aggregate
demand is completely driven by asset holders.
If participation is restricted below a certain threshold, the predictions are strengthened: as
the share of non-asset holders increases, the link between interest rates and aggregate demand
becomes stronger, and monetary policy is more effective; we label this case ‘standard aggregate
demand logic’, (SADL). However, when participation is restricted beyond a given threshold,
standard theoretical prescriptions or predictions are reversed. First, the ‘IS curve’ has a positive
slope: current aggregate output is positively related to real interest rates; we dub this case ‘inverted
aggregate demand logic’, (IADL). Secondly, the ‘Taylor principle’ [45] is inverted: the central
bank needs to adopt a passive policy rule whereby it increases the nominal interest rate by less
than inflation (i.e. decreases the real interest rate), for policy to be consistent with a unique
rational expectations equilibrium. 6 Relatedly, an interest rate peg can also lead to a determinate
equilibrium. Thirdly, the welfare-maximizing optimal policy problem can still be cast in a linearquadratic
framework; but an expectations-based instrument rule implementing the discretionary
optimum ought to be passive. Importantly, however, there exist targeting rules that implement
optimal policy under commitment (or timeless-optimal policy in the sense of Woodford [46])
and lead to equilibrium determinacy regardless of the degree of asset markets participation. And
finally, the effects of some shocks are overturned (for example, unanticipated positive shocks
to interest rates are expansionary). In the limit (when nobody holds assets), aggregate demand
ceases to be linked to interest rates and monetary policy becomes ineffective. The required share
of non-asset holders for these results to hold can be compared to empirical estimates or to direct
data on asset holding.
The paper closest related to ours is Galí, Lopez-Salido and Valles [21] (hereinafter GLV);
that paper studies determinacy properties of interest rate rules in a sticky-price model in which
a fraction of agents does not hold physical capital and follows a ‘rule-of-thumb’. The general
message of that paper is that the Taylor principle is not a good guide for policy under some
parameterizations. Namely, GLV argue that if the central bank responds to current inflation via a
simple Taylor rule, when the share of ‘rule-of-thumb’ agents is high enough the Taylor principle
is strengthened: the response to inflation needs to be higher than in the benchmark model. On the
contrary, for a rule responding either to past or future expected inflation, GLV suggest, based on
numerical simulations, that for a high share of non-asset holders the policy rule needs to violate
the Taylor principle to ensure equilibrium uniqueness.The aspects that differentiate our paper from GLV pertain to three issues: assumptions, girth
and, where the focus of the paper does overlap, message. Concerning assumptions, we model
the asset market explicitly and emphasize its interaction with the labor market, which is at the
core of the intuition for all our results; any discussion of this is absent from GLV. We also
abstract from physical capital accumulation and non-separability in the utility function, since
these features can by themselves dramatically change determinacy properties of interest rate
rules. 7 This simplification allows us to focus on the role of LAMP exclusively, derive all results
analytically, and hence provide clear economic intuition for them. Concerning girth, determinacy
properties of interest rate rules are only a subset of our paper’s focus, which regards these issues
together with others (most notably: welfare-based optimal monetary policy) as part of a more
general theme having to do with LAMP’s influence on the aggregate demand side. Finally, within
the issue of determinacy properties, our conclusions are different from GLV’s as follows.We show
analytically that an inverted Taylor principle holds in general when asset market participation is
restricted enough. This result depends only to a small extent on whether the rule is specified in
terms of current or expected future inflation. As discussed in text in more detail, this is in contrast to
GLV who, while having noted the possibility to violate the Taylor principle for a forward-looking
rule, also argue that a strengthening of the Taylor principle is required for a contemporaneous
rule to result in equilibrium uniqueness. A very strong response to current inflation would also
insure determinacy in our model, but we find the implied coefficient is higher than any plausible
estimates and makes policy non-credible.We also show how the Taylor principle can be restored
by either an appropriate response to output or via distortionary redistributive taxation of dividend
income.
Our results can be perhaps most relevant for analyzing (i) developing economies, in which
participation in asset markets is notoriously limited; (ii) historical episodes during which even
developed economies experienced exceptionally low asset market participation. Regarding the
latter, many authors have argued that policy before Volcker was ‘badly’ conducted along one or
several dimensions, which led to worse macroeconomic performance as compared to the Volcker–
Greenspan era. One such argument relies upon the estimated pre-Volcker policy rule non-fulfilling
the ‘Taylor principle’, hence containing the seeds of macroeconomic instability driven by nonfundamental
uncertainty [14,33]. Our results imply that limited asset market participation can
potentially provide a very different interpretation of these results. If during the pre-Volcker sample
asset market participation was so limited to bring the economy to the IADL region whereby the
inverted Taylor principle is a good policy prescription, Federal Reserve policy may have been
better conducted than is suggested by the benchmark, full-participation New Keynesian model.
Indeed, in that case a policy that violated the Taylor principle induced equilibrium determinacy
and macroeconomic performance can be interpreted relying only on fundamental shocks. In
particular, the higher inflation volatility during the pre-Volcker sample relative to the later period
can be shown to occur as an unique equilibrium outcome in a simple calibrated version of our
IADL economy; we perform this exercise in Section 6. A companion paper (Bilbiie and Straub
[9]) described in some detail in the same section provides empirical support for this hypothesis
by estimating a richer version of this paper’s model using Bayesian techniques.
The rest of the paper is organized as follows. Sections 2 and 3 introduce the LAMP general
equilibrium model and its reduced log-linear form, and discuss our core results intuitively.A discussion of the labor market equilibrium useful for further intuition is also presented. Section
4 outlines the ‘inverted Taylor principle’ and discusses ways to restore Keynesian logic, and
the Taylor principle. Section 5 analyzes welfare-maximizing optimal monetary policy, Section 6
outlines some positive implications of our model and Section 7 concludes. Most technical details
are contained in the Appendices.

نتیجه گیری انگلیسی

The above analysis has shown how limited asset markets participation (LAMP), by changing
aggregate demand’s sensitivity to interest rates nonlinearly, changes monetary policy prescriptions
likewise. Despite their insensitivity to real interest rates, non-asset holders affect the sensitivity of
aggregate demand to interest rates since these agents are oversensitive to realwage variations. Real
wages are related to interest rates through the labor supply decision of asset holders and the way
this interacts with their asset holdings (through income effects and intertemporal substitution).
Their asset income, in turn, consists of dividend income and is also related to real wages which
are equal to marginal costs. Therefore, non-asset holders and asset holders interact through the
interdependent functioning of labor and asset markets. These interactions can either strengthen
(if participation is not ‘too’ limited) or overturn the systematic link between interest rates on
aggregate demand. The latter case occurs if the share of non-asset holders is high enough and/or
and the elasticity of labor supply is low enough. This is the main mechanism identified by this
paper to make monetary policy analysis dramatically different when compared to a standard
full-participation case whereby aggregate demand is completely driven by asset holders. This
paper develops an analytical framework incorporating the foregoing insight and uses it to study in
detail the dynamics of a simple general equilibrium model, the determinacy properties of interest
rate rules and optimal, welfare-based, monetary policy. Its aim is to make a contribution to the
literature emphasizing the role of LAMP in shaping macroeconomic policy and helping towards
a better understanding of the economy. In that respect, we just seek to add to a new developing
literature analyzing the role of non-asset holders in macroeconomic dynamic general equilibrium
models (see [34,1], or [20]).
Our results have clear normative implications. In a nutshell, central bank policy should be
pursued with an eye to the aggregate demand side of the economy. Empirical results on consumption
behavior and asset market participation, on the one hand, and labor supply elasticity and the
degree of monopoly power in goods markets, on the other, would become an important part of
the policy input. While the degree of development of financial markets may well make this not a
concern in present times in the developed economies, central banks in developing countries with
low participation in financial markets might find this of practical interest. The theoretical results
hinting to such policy prescriptions are related to limited participation beyond a certain thresholdinducing an inversion of SADL. Namely, the slope of the IS curve changes sign, and an inverted
Taylor principle applies generally: the central bank needs to adopt a passive policy rule to ensure
equilibrium uniqueness and rule out self-fulfilling, sunspot-driven fluctuations. Moreover, optimal
time-consistent monetary policy also requires that the central bank move nominal rates such that
real rates decline (thereby containing aggregate demand). The effects and transmission of shocks
are also radically modified. Importantly, however, we have shown that commitment to a targeting
rule that implements timeless-optimal policy delivers equilibrium determinacy regardless of the
degree of asset markets participation.We view this as an additional argument in favor of adopting
targeting rules purported to implement commitment policy.
In this paper we modeled limited asset market participation in a very simple way, and were
as a result able to isolate and study its implications for monetary policy analytically in the same
type of framework used in standard, full-participation analyses. This simplicity (shared with the
rest of the literature), while justified on tractability grounds, also implies that many realistic
features have been left out. For instance, one could try to break the link between asset markets
participation and consumption smoothing behavior, which this paper assumed. Another important
extension would endogenize the decision to participate in asset markets. Lastly, an empirical
assessment of limited participation, its dynamics and implications at the aggregate level, is in our
view a necessary step for understanding business cycles. We pursue such extensions in current
work.